The NCSSM conference ended around 1 today and my flight back home got cancelled due to snow. Luckily, a former student of mine lives nearby and he graciously has offered his place for me to sleep. We also had a great night out catching up.
I’ve been thinking more about @JustinAion’s quote from a couple of blog posts ago. He said that he only feels like he is teaching when he is answering student questions or going over examples. After the sessions here at NCSSM I am even more committed to fighting that urge – the one that Justin put his finger on. I want to be more invisible, give my students more room. Ask more than tell. I want to analyze their thinking more than their answers. I want to think deeply about their questions and misunderstandings. I hope to get better at this and I’ll report back as I try some new ideas out about how to do this.
A quick aside based on a conversation before one of the sessions. A teacher behind me was talking about his daughter Maya who had recently learned to spell her name reliably. He mentioned that she had also recently learned that her middle name was Sage and she decided that she’d rather be called Sage. She was still spelling her name the same way but she was announcing that she had written Sage now, instead of Maya. I have to imagine that the set of alphabet symbols that we would read as Maya simply read to her as her name. If her name is now Sage, then those symbols mean Sage. I was reminded of my own 4 year old who we call Mo. Over the past five months Mo’s ‘signature’ has evolved from OW to WO to OM to MO. However, whenever she sees something with her name on it she simply says it is hers. She seems to see no difference between them. I wonder how similar this is to some of our students writing down things like (x + y)^2 = x^2 + y^2 and not having any recognition that it does not match anything we’ve written.
8 thoughts on “Late Night Reflections”
I think it’s fascinating to think about how student decode mathematics. It’s very difficult to fully understand someone else’s though process unless they tell it to us. I think you may be on to something critical when it comes to student thinking about the symbols and rules of mathematical convention.
I shall ponder.
The telling is such a challenge for so many of my students. How can we help them find their own words at first and then have those words approach the correct, formal language? Such a challenge.
I think it just takes practice, asking the kids to explain their thinking again and again, then slowly correcting the vocab in that thinking. It will make them nuts, but eventually get them where we need them to be.
I was doing a demo lesson on word problems using a scientific notation and a problem set I found from NASA. The target was advanced 7th graders, and I was teaching them to decode text. I was a little astounded by how little knowledge they had of things like mass, proton, and plasma…That being said, by the time the lesson was done, the students had had some success in solving the problems and they were loving it. The point is, I used a tape diagram to explain the problem in using a compare/contrast model with a simpler example (common student ages). The different representation, combined with a visual made a strange, “ooooo” noise from the audience. I guess if we can find a correct representation it makes clear what it is the problems are asking. In kind to the point you made here.
That ‘oooo’ sound is the sound of roaring success, isn’t it?
Yes it was (=
All I can say is how jealous I am you got to go to such an amazing conference. (: I would love to have a giant “Math Nerd Unite” somewhere. I’d stand in line for that conference.
I feel VERY fortunate to have obtained funding for this conference. My school has been generous with this kind of support.